A282766
n/2 analog of Keith numbers.
Original entry on oeis.org
50, 642, 1284, 1926, 2292, 5088, 29828, 42922, 53046, 95968, 512050, 1043160, 1723714, 14819056, 154860206, 159251186, 752516578, 946218018, 54728972948
Offset: 1
642/2 = 321:
3 + 2 + 1 = 6;
2 + 1 + 6 = 9;
1 + 6 + 9 = 16;
6 + 9 + 16 = 31;
9 + 16 + 31 = 56;
16 + 31 + 56 = 103;
31 + 56 + 103 = 190;
56 + 103 + 190 = 349;
103 + 190 + 349 = 642.
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with(numtheory): P:=proc(q,h,w) local a, b, k, n, t, v; v:=array(1..h);
for n from 1/w by 1/w to q do a:=w*n; b:=ilog10(a)+1; if b>1 then
for k from 1 to b do v[b-k+1]:=(a mod 10); a:=trunc(a/10); od; t:=b+1; v[t]:=add(v[k], k=1..b);
while v[t]
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With[{n = 2}, Select[Range[10 n, 10^6, n], Function[k, Last@ NestWhile[Append[Rest@ #, Total@ #] &, IntegerDigits[k/n], Total@ # <= k &] == k]]] (* Michael De Vlieger, Feb 27 2017 *)
A282769
n/7 analog of Keith numbers.
Original entry on oeis.org
301, 602, 1113, 4942, 478205, 23942940, 47885880, 178114489749
Offset: 1
1113/7 = 159:
1 + 5 + 9 = 15;
5 + 9 + 15 = 29;
9 + 15 + 29 = 53;
15 + 29 + 53 = 97;
29 + 53 + 97 = 179;
53 + 97 + 179 = 329;
97 + 179 + 329 = 605;
179 + 329 + 605 = 1113.
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with(numtheory): P:=proc(q,h,w) local a, b, k, n, t, v; v:=array(1..h);
for n from 1/w by 1/w to q do a:=w*n; b:=ilog10(a)+1; if b>1 then
for k from 1 to b do v[b-k+1]:=(a mod 10); a:=trunc(a/10); od; t:=b+1; v[t]:=add(v[k], k=1..b);
while v[t]
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With[{n = 7}, Select[Range[10 n, 10^6, n], Function[k, Last@ NestWhile[Append[Rest@ #, Total@ #] &, IntegerDigits[k/n], Total@ # <= k &] == k]]] (* Michael De Vlieger, Feb 27 2017 *)
A282767
n/3 analog of Keith numbers.
Original entry on oeis.org
45, 609, 1218, 1827, 3213, 21309, 28206, 29319, 31917, 39333, 47337, 78666, 102090, 117999, 204180, 406437, 302867592, 4507146801, 5440407522
Offset: 1
609/3 = 203:
2 + 0 + 3 = 5;
0 + 3 + 5 = 8;
3 + 5 + 8 = 16;
5 + 8 + 16 = 29;
8 + 16 + 29 = 53;
16 + 29 + 53 = 98;
29 + 53 + 98 = 180;
53 + 98 + 180 = 331;
98 + 180 + 331 = 609.
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with(numtheory): P:=proc(q,h,w) local a, b, k, n, t, v; v:=array(1..h);
for n from 1/w by 1/w to q do a:=w*n; b:=ilog10(a)+1; if b>1 then
for k from 1 to b do v[b-k+1]:=(a mod 10); a:=trunc(a/10); od; t:=b+1; v[t]:=add(v[k], k=1..b);
while v[t]
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With[{n = 3}, Select[Range[10 n, 10^6, n], Function[k, Last@ NestWhile[Append[Rest@ #, Total@ #] &, IntegerDigits[k/n], Total@ # <= k &] == k]]] (* Michael De Vlieger, Feb 27 2017 *)
Showing 1-3 of 3 results.
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